Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
2006-02-17
Phys.Rev. D73 (2006) 044034
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
30 pages
Scientific paper
10.1103/PhysRevD.73.044034
Accurate calculation of the gradual inspiral motion in an extreme mass-ratio binary system, in which a compact-object inspirals towards a supermassive black-hole requires calculation of the interaction between the compact-object and the gravitational perturbations that it induces. These metric perturbations satisfy linear partial differential equations on a curved background spacetime induced by the supermassive black-hole. At the point particle limit the second-order perturbations equations have source terms that diverge as $r^{-4}$, where $r$ is the distance from the particle. This singular behavior renders the standard retarded solutions of these equations ill-defined. Here we resolve this problem and construct well-defined and physically meaningful solutions to these equations. We recently presented an outline of this resolution [E. Rosenthal, Phys. Rev. D 72, 121503 (2005)]. Here we provide the full details of this analysis. These second-order solutions are important for practical calculations: the planned gravitational-wave detector LISA requires preparation of waveform templates for the expected gravitational-waves. Construction of templates with desired accuracy for extreme mass-ratio binaries requires accurate calculation of the inspiral motion including the interaction with the second-order gravitational perturbations.
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